Highest Common Factor of 360, 602, 729 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 360, 602, 729 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 360, 602, 729 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 360, 602, 729 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 360, 602, 729 is 1.

HCF(360, 602, 729) = 1

HCF of 360, 602, 729 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 360, 602, 729 is 1.

Highest Common Factor of 360,602,729 using Euclid's algorithm

Highest Common Factor of 360,602,729 is 1

Step 1: Since 602 > 360, we apply the division lemma to 602 and 360, to get

602 = 360 x 1 + 242

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 242 and 360, to get

360 = 242 x 1 + 118

Step 3: We consider the new divisor 242 and the new remainder 118, and apply the division lemma to get

242 = 118 x 2 + 6

We consider the new divisor 118 and the new remainder 6,and apply the division lemma to get

118 = 6 x 19 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 360 and 602 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(118,6) = HCF(242,118) = HCF(360,242) = HCF(602,360) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 729 > 2, we apply the division lemma to 729 and 2, to get

729 = 2 x 364 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 729 is 1

Notice that 1 = HCF(2,1) = HCF(729,2) .

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Frequently Asked Questions on HCF of 360, 602, 729 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 360, 602, 729?

Answer: HCF of 360, 602, 729 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 360, 602, 729 using Euclid's Algorithm?

Answer: For arbitrary numbers 360, 602, 729 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.